Which table represents a linear function?

Answer:

1/8 tablespoons

Step-by-step explanation:

Since the child needs to take 1/2 tablespoons off medicine per day in 4 equal doses, you will divide the 1/2 tablespoons into 4 equal doses, so you need to divide by 4.

You can do this by multiplying 1/2 by 1/4.

\(\frac{1}{2} * \frac{1}{4} = \frac{1}{8}\)

Answer:

it would be 1/8

Step-by-step explantion:

simply divide

1/2÷4

=1/8

(that should be right)

Answer:

Integrate( sqrt(9-x^2) from x=-3 to x=3)

Step-by-step explanation:

The equation for a full circle is (x-h)^2+(y-k)^2=r^2 where (h,k) is center and radius is r.

Your center, your (h,k) is (0,0). Your radius, your r, is 3.

So your equation is (x-0)^2+(y-0)^2=3^2 or more simply x^2+y^2=9.

We also must consider we don't have full circle.

Solving for y will give us the circle in terms of top half if we take positive values and bottom half if we take negative values. Since y is positive in the picture, you only see top half, we will only take the positive cases for y.

Subtracting x^2 on both sides gives: y^2=9-x^2

Square root both sides: y= sqrt(9-x^2)

(I did not choose -sqrt(9-x^2) because again y is positive).

So the x's in the picture range from -3 to 3.

The integral is therefore,

Integrate( sqrt(9-x^2) from x=-3 to x=3)

Answer:

Read

Step-by-step explanation:

Mean: add all the values and divide by the number of values

Median: when in order from least to greatest, the middle value

Mode: The value that ocoours most often

Answer:

-5x-6

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hello, I believe that we can consider a different from 0.

By definition of the roots we can write.

\(ax^2+bx+c=a(x-\alpha)(x-\beta)=a(x^2-(\alpha + \beta)x+\alpha \cdot \beta)\\\\\text{So we can say that:}\\\\\alpha + \beta = \dfrac{-b}{a}\\\\\alpha \cdot \beta=\dfrac{c}{a}\\\\\text{So the expected quadratic equation is}\\\\(x+\dfrac{b}{a})(x-\dfrac{c}{a})=0\\\\<=> \Large \boxed{\sf \bf \ (ax+b)(ax-c)=0 \ }\)

Thank you

Answer:

I put down my steps in the comment section. If you still don't understand just comment to me.

Step-by-step explanation:

Answer: I answered 6-11

Step-by-step explanation:

Answer:

-5

Step-by-step explanation:

m= -1

7(-1)+4-(-1)(7)(-1)+4-(-1)

-7+-3+5

=-5

Answer: ∠ 5

Step-by-step explanation:

I got you fam

Answer: V≈42.88in³

Step-by-step explanation: i might be wrong but let me know

Answer:

a =b = \(\frac{5\sqrt{5} }{5}\)

Step-by-step explanation:

\(a^{2} +b^{2} = 5 ^{2}\)

a = b

\(2a^{2} = 5 ^{2}\)

\(2a^{2} = 25\\\)

\(a^{2} = \frac{25}{5}\)

a = \(\frac{5}{\sqrt{5} }\)

must rationalize...

a =b = \(\frac{5\sqrt{5} }{5}\)

Answer:

[0, infinity)

[0, size of gas tank)

The probability that Steve will get a nine on the next card he is dealt is 4/47.  Steve and Cathy are playing a card game with a standard deck of 52 playing cards. After Cathy is dealt an ace and a four and Steve is dealt a jack, there are 49 cards left in the deck. Out of the remaining cards, there are three aces.

If Steve gets an ace on the next card he is dealt, he will win. The probability of this happening is 3/49, as there are three aces left in the deck out of a total of 49 cards remaining.

After Steve gets a two and Cathy gets a five, there are now 47 cards left in the deck. The probability of Steve getting a nine on the next card he is dealt is 4/47, as there are four nines left in the deck out of a total of 47 cards remaining.

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By using scientific notation we calculated (2.3\(\times\)10⁵)(1.5 \(\times\)10⁴) we got 345 \(\times\)10⁷.

Given that,

(2.3\(\times\)10⁵)(1.5 \(\times\)10⁴)

By using scientific notation

The scientific notation allows us to express extremely large or extremely small numbers by multiplying them by single-digit integers and by 10 raised to the power of the corresponding exponent. The exponent is either positive or negative depending on how big or little the number is.

Now, we calculate

(2.3\(\times\)10⁵)=2.5\(\times\)100000=230000

(1.5 \(\times\)10⁴)=1.5\(\times\)10000=15000

Now,

=230000\(\times\)15000

=3450000000

=345 \(\times\)10⁷

Therefore, By using scientific notation we calculated (2.3\(\times\)10⁵)(1.5 \(\times\)10⁴) we got 345 \(\times\)10⁷.

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a) r = 40 units and,  p = 200 units units each chemical ( P and R ) should be "purchased" to maximize production of chemical Z subject to the budgetary constraint.

b) the maximum number of units of chemical Z under the given budgetary conditions Z = 3400√20 units.

Here, we have,

To maximize the production of chemical Z subject to the budgetary constraint, we need to set up an optimization problem.

Let's solve it step by step:

A) We need to determine the number of units of chemicals P and R that should be purchased. Let's denote them as p and r, respectively.

The cost equation is given by: Cost = 200p + 1200r.

The budget constraint is: Cost ≤ 720,000.

Substituting the cost equation into the budget constraint, we have: 200p + 1200r ≤ 720,000.

We also have the production equation: z = 80\(p^{0.9}\) * \(r^{0.1}\).

Now, we can set up the optimization problem:

Maximize z = 80\(p^{0.9}\) * \(r^{0.1}\).

Subject to: 200p + 1200r ≤ 720,000

To solve this problem, we can use the method of Lagrange multipliers or other optimization techniques. However, since the variables p and r are raised to fractional powers, the calculation becomes quite complex. Therefore, it is recommended to use specialized software or tools to find the optimal values of p and r.

solving we get,

r = 40 units

p = 400 - 5r = 200 units

Z = 3400√20 units.

B) Once we find the optimal values of p and r, we can substitute them back into the production equation z = 80\(p^{0.9}\) * \(r^{0.1}\). to determine the maximum number of units of chemical Z under the given budgetary conditions. The result will depend on the optimal values obtained in part A.

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Answer:

The starting height of the chairlift

Answer:

=−28

Step-by-step explanation:

To determine which amounts of postage can be formed using just 4-cent and 11-cent stamps, we need to find all non-negative integer solutions to the equation 4x + 11y = z, where x and y are non-negative integers representing the number of 4-cent and 11-cent stamps used, respectively, and z is the total amount of postage. We can use a combination of trial and error and modular arithmetic to find all possible values of z.

(b) Proof by mathematical induction:

Base case: For z = 0, there are no stamps used, so the equation is satisfied. Thus, 0 can be formed using just 4-cent and 11-cent stamps.

Inductive step: Assume that all integers from 0 to k can be formed using just 4-cent and 11-cent stamps, where k is a non-negative integer. We want to show that k+1 can also be formed.

If k+1 is divisible by 4 or 11, then we can form it using only 4-cent or 11-cent stamps, respectively. Otherwise, we can use the inductive hypothesis to show that k-4 and k-11 can be formed using just 4-cent and 11-cent stamps, respectively. Then we can add one 4-cent or one 11-cent stamp to form k+1.

Therefore, by mathematical induction, all non-negative integers can be formed using just 4-cent and 11-cent stamps.

(c) Proof by strong induction:

Base case: For z = 0, there are no stamps used, so the equation is satisfied. Thus, 0 can be formed using just 4-cent and 11-cent stamps.

Inductive step: Assume that all integers from 0 to k can be formed using just 4-cent and 11-cent stamps, where k is a non-negative integer. We want to show that k+1 can also be formed.

If k+1 is divisible by 4 or 11, then we can form it using only 4-cent or 11-cent stamps, respectively. Otherwise, we can use the inductive hypothesis to show that all integers from k-10 to k-1 can be formed using just 4-cent and 11-cent stamps. Then we can add two 4-cent stamps and one 11-cent stamp to form k+1.

The inductive hypothesis in this proof differs from that in the proof using mathematical induction in that we assume that all integers from k-10 to k-1 can be formed, rather than just k-4 and k-11. This is because we need to show that all integers up to k+1 can be formed, and we may need to use more than one 4-cent or 11-cent stamp to form some of the intermediate values.

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a liner pair is the pair of adjacent angles formed when two line intersect

Answer:

6264

Step-by-step explanation:

(2+2)×2-11×+28 6×2

= 6264

Answer:

I...what kinda question is dis

Answer:

x=33/5

Step-by-step explanation:

Let's solve your equation step-by-step.

2x+4/5 −6=8

Step 1: Simplify both sides of the equation.

2x+4/5−6=8

2x+4/5+−6=8

(2x)+(4/5+−6)=8(Combine Like Terms)

2x+−26/5=8

2x+−26/5=8

Step 2: Add 26/5 to both sides.

2x+−26/5+26/5=8+26/5

2x=66/5

Step 3: Divide both sides by 2.

2x/2=66/5/2

x=33/5

Answer:

12

Step-by-step explanation:

Answer:

1) 12 boxes

2) 3, 6, 12

3) 12

4) 110 degrees

Step-by-step explanation:

1) Count the rectangles. Multiply the length of the rectangle in boxes to the width of rectangle in boxes.

Length: 4 boxes

Width: 3 boxes

4 x 3 = 12

12 boxes

2)

10% of 30 is 0.1 times 30.

0.1 x 30 = 30/10 = 3

20% of 30 is 0.2 times 20.

0.2 x 30 = 30/5 = 6

40% of 30 is 0.4 times 20.

0.4 x 30 = 30/2.5 = 12

3) Count the cubes. Reminder there are 2 boxes you cannot see.

Top Layer: 2

Middle Layer: 4

Back Bottom Layer: 4

Front Bottom Layer: 2

2 + 4 + 4 + 2 = 12

4) I cannot see the semicircle clearly, but I do know that a circle is 360 degrees. A semicircle, half of a circle, is 180 degrees.

180/18 (The angle of each section)

10

11 Sections

10 x 11 = 110

The limit of the function lim(θ→0) sin(2θ)/θ can be estimated by using a graph.

To estimate this limit graphically, you would first plot the function y = sin(2θ)/θ on a graph with the x-axis representing θ and the y-axis representing the function value. Since θ is measured in radians, make sure your graph is set to radians as well. As θ approaches 0, observe the behavior of the function.

Based on the graph, you will notice that the function approaches a value of 2 as θ approaches 0. Therefore, lim(θ→0) sin(2θ)/θ ≈ 2.

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Jeff's savings account, which earns simple interest, has a total amount of 10,405.2 today after 2 years.

Simple interest is given by the formula:

SI = PTR/100

Where SI = simple interest

P = principal

R = interest rate (in percentage)

T = time duration (in years)

If he deposited 8700 into the account 2 years ago and earns interest at a rate of 9.8%, then using the formula, the amount of interest earned can be determined.

SI = PTR/100

SI = 8700(2)(9.8)/100

SI = 1705.2

To get the total amount on his account, add the interest earned to the principal amount he deposited.

total amount = 8700 + 1705.2

total amount = 10,405.2

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Using the probability concept, it is found that there is a 0.8456=  84.56% probability that client A lives to be 20 years old.

A probability is the chances of happening of any event from the random variables. A probability is the number of desired outcomes divided by the number of total outcomes, that is:

\(P=\dfrac{D}{T}\)

In this problem:

Out of 100,000 clients, 84,560 lives to age 64, hence

Then:

\(P=\dfrac{84560}{100000}=84.56\%\)

There is a 0.8456= 84.56% probability that client A lives to be 30 years old.

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Answer:

Fraction A (a/b). Fraction B (c/d)  Find what is fraction addition for given input data  Therefore, find lcm for two denominators (3, 2) = 6  The result is the sum of numerators over the LCM;; Simplify the result if needed.  5/2 + 3/7, 41/14.

The corresponding constant k in the exponential decay function is given by k = -(ln2)/T.

The exponential decay function for a radioactive substance can be expressed as:

N(t) = N₀\(e^{(-kt),\)

where N₀ is the initial number of radioactive atoms, N(t) is the number of radioactive atoms at time t, and k is the decay constant.

The half-life, T, of the substance is the time it takes for half of the radioactive atoms to decay. At time T, the number of radioactive atoms remaining is N₀/2.

Substituting N(t) = N₀/2 and t = T into the equation above, we get:

N₀/2 = N₀\(e^{(-kT)\)

Dividing both sides by N₀ and taking the natural logarithm of both sides, we get:

ln(1/2) = -kT

Simplifying, we get:

ln(2) = kT

Solving for k, we get:

k = ln(2)/T

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The derivation of the formula k = ln2/t gives us the half life of the isotope.

The amount of time it takes for half of a sample's radioactive atoms to decay and change into a different element or isotope is known as the half-life. It is a distinctive quality of every radioactive substance and is unaffected by the initial concentration.

We know that;

\(N=Noe^-kt\)

Now if we are told that;

N = amount of radioactive substance at time = t

No = Initial amount of radioactive substance

k = decay constant

t = time taken

Then at the half life it follows that N = No/2 and we have that;

\(No/2 =Noe^-kt\\1/2 = e^-kt\)

ln(1/2) = -kt

-ln2 = -kt

k = ln2/t

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Answer:

there is no number to plug into x cause you can't have a negative number if it is absolute value cause that makes everything positive

Answer:

f = 4

Step-by-step explanation:

Step 1: Distribute

-11f = 7 - 14f + 5

Step 2: Combine like terms

-11f = 12 - 14f

Step 3: Add 14f to both sides

3f = 12

Step 4: Divide both sides by 3

f = 4

Answer:

F = 4

solution,

-11f=7(1-2f )+5

Or -11 f = 7-14 f +5

Or -11 f +14 f = 5+7

Or 3 f = 12

Or f=12/3

F = 4

hope this helps...

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